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# If x and y are integers greater than 1, is x a multiple of

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Director
Joined: 06 Sep 2006
Posts: 736
If x and y are integers greater than 1, is x a multiple of [#permalink]

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22 Jul 2007, 21:18
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If x and y are integers greater than 1, is x a multiple of y?

1) 3y^2 + 7y = x

2) x^2 - x is a multiple of y.

Share your solutions guys, just not the answers!
Senior Manager
Joined: 04 Jun 2007
Posts: 345
Re: DS - number properties [#permalink]

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22 Jul 2007, 21:38
asaf wrote:
If x and y are integers greater than 1, is x a multiple of y?

1) 3y^2 + 7y = x

2) x^2 - x is a multiple of y.

Share your solutions guys, just not the answers!

A for me.

stmt 1: y*(3y+7) = x
or, 3y+7 = x/y
Since, 3y+7 must be an integer, so too must be x/y. Hence, x is a multiple of y. sufficient.

stmt 2: x*(x-1) = ky (k is some integer greater than 0)
This is not sufficient. e.g. x=3 and y=2; x=4 and y=2
Senior Manager
Joined: 28 Jun 2007
Posts: 454

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22 Jul 2007, 21:46
I think E.

I cant share my solution because I couldn't solve this easily. 1 and 2 alone look insufficient. So I made an educated guess.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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22 Jul 2007, 22:33
St1:
y(3y+7) = x
3y+7 = x/y
Since 3y + 7 must be integer, then x/y must be integer and x must be a multiple of y if x/y = integer.

St2:
x(x-1) = ym
(x/y)(x-1) = m
Since m is an integer, (x-1) is an integer then x/y must be an integer for the relationship to hold. So x must be a multiple of y.

Ans D
Senior Manager
Joined: 04 Jun 2007
Posts: 345

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23 Jul 2007, 00:28
ywilfred wrote:
St1:
y(3y+7) = x
3y+7 = x/y
Since 3y + 7 must be integer, then x/y must be integer and x must be a multiple of y if x/y = integer.

St2:
x(x-1) = ym
(x/y)(x-1) = m
Since m is an integer, (x-1) is an integer then x/y must be an integer for the relationship to hold. So x must be a multiple of y.

Ans D

I do not think statement 2 can be sufficient. (x-1) and not x may be a multiple of y.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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23 Jul 2007, 01:22
sumande wrote:
ywilfred wrote:
St1:
y(3y+7) = x
3y+7 = x/y
Since 3y + 7 must be integer, then x/y must be integer and x must be a multiple of y if x/y = integer.

St2:
x(x-1) = ym
(x/y)(x-1) = m
Since m is an integer, (x-1) is an integer then x/y must be an integer for the relationship to hold. So x must be a multiple of y.

Ans D

I do not think statement 2 can be sufficient. (x-1) and not x may be a multiple of y.

yeah.. missed that point. Ouch!
Director
Joined: 08 Jun 2007
Posts: 573
Re: DS - number properties [#permalink]

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23 Jul 2007, 08:27
asaf wrote:
If x and y are integers greater than 1, is x a multiple of y?

1) 3y^2 + 7y = x

2) x^2 - x is a multiple of y.

Share your solutions guys, just not the answers!

I am going with B .

1. y(3y +7 ) = x . I think it means y is a multiple of x and not as it is asked "is x a multiple of h?" So insufficient.

2. x(x-2) = ky . This proves x is a multiple of y .Sufficient

So B .

BTW , whats the OA ?
Senior Manager
Joined: 04 Jun 2007
Posts: 345
Re: DS - number properties [#permalink]

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23 Jul 2007, 08:46
ashkrs wrote:
asaf wrote:
If x and y are integers greater than 1, is x a multiple of y?

1) 3y^2 + 7y = x

2) x^2 - x is a multiple of y.

Share your solutions guys, just not the answers!

I am going with B .

1. y(3y +7 ) = x . I think it means y is a multiple of x and not as it is asked "is x a multiple of h?" So insufficient.

2. x(x-2) = ky . This proves x is a multiple of y .Sufficient

So B .

BTW , whats the OA ?

The question clearly asks if "x is a multiple of y" !!
Director
Joined: 08 Jun 2007
Posts: 573
Re: DS - number properties [#permalink]

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24 Jul 2007, 08:19
sumande wrote:
ashkrs wrote:
asaf wrote:
If x and y are integers greater than 1, is x a multiple of y?

1) 3y^2 + 7y = x

2) x^2 - x is a multiple of y.

Share your solutions guys, just not the answers!

I am going with B .

1. y(3y +7 ) = x . I think it means y is a multiple of x and not as it is asked "is x a multiple of h?" So insufficient.

2. x(x-2) = ky . This proves x is a multiple of y .Sufficient

So B .

BTW , whats the OA ?

The question clearly asks if "x is a multiple of y" !!

I think I am getting my terminology wrong. Please correct me .

If X is a multiple of Y .
I understand that as : if Y = 36 then X can be 1 2 3 4 6 12 18.
Intern
Joined: 12 Jun 2007
Posts: 20

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24 Jul 2007, 12:05
Clear A.
x= y(3y+7) meaning x is a multiple of y.
Intern
Joined: 12 May 2007
Posts: 23

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24 Jul 2007, 13:10
y*(3y+7)=x sufficient

x(x-1)= y ; this would mean that y is a multiple of x. it is not the question?

do you have official answer??
Senior Manager
Joined: 21 Jun 2006
Posts: 282

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25 Jul 2007, 08:59
I say A

statment in A can be factorized into
y(3y+7)=x
3y+7 must be an integer as y >1 and int

B

x(x-1)=ky

where k is int

therefore, x = (k/x-1)y

k/x-1 need not be an integer

say if x =18, x-1 = 17 and k =5 then x is not a multiple of y
Hence INSIFF
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

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25 Jul 2007, 09:10
If x and y are integers greater than 1, is x a multiple of y?

1) 3y^2 + 7y = x

2) x^2 - x is a multiple of y.

OK lets see...

x/y=N where N is an integer?

1) Y(3Y+7)=x; x/y= (3Y+7) we are told x and y are integers...therefor RHS is an integer...which inturn means RHS is an integer...therefore X is a multiple..sufficient..

2) x(x-1)=y/N ...we dont know if X or X-1 is the multiple of Y..therefore insufficient...

A it is..
Director
Joined: 26 Feb 2006
Posts: 899
Re: DS - number properties [#permalink]

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25 Jul 2007, 09:57
asaf wrote:
If x and y are integers greater than 1, is x a multiple of y?

1) 3y^2 + 7y = x
2) x^2 - x is a multiple of y

A too...........

from 1: 3y^2 + 7y = x
y (3y + 7) = x
in this case, 3y+7 is an integer. so x is a multiple of x.

from 2: x^2 - x = yk
x (x -1) = yk
x (x -1) = yk
k could be or could not be x or x-1. suppose, x = 4, x-1=3, k =1 and y = 12. in this case x is not a multiple of y. if x = 4, x-1 = 3, y = 3 and k =4, x is a multiple of y.
Re: DS - number properties   [#permalink] 25 Jul 2007, 09:57
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# If x and y are integers greater than 1, is x a multiple of

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